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Geometric Construction of Aragón TV Logo

Geometric Construction of Aragón TV Logo
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2020-01-23 03:04
CirclePolygonAngleVectorGeometric Construction
This example demonstrates the geometric construction of a complex 2D shape, particularly involving circles, vectors, and angles. Key math concepts include 2D vectors, angle calculations, circle properties, and geometric constructions. GeoGebra commands and objects used in the construction are Line, OrthogonalLine, Vector, OrthogonalVector, Midpoint, LineBisector, Mirror, Intersect, CircleArc, Polygon, and CircleSector. Suitable for high school and above students to understand geometric constructions and spatial relationships.

GeoGebra Commands & Parameters

  1. Line(A, B) → s
  2. OrthogonalLine(A, s) → b
  3. Vector(A, B) → u
  4. OrthogonalVector(u) → v
  5. OrthogonalLine(A_1, b) → r
  6. Midpoint(A_1, A) → J
  7. OrthogonalLine(Q_1, b) → m_2
  8. LineBisector(A, B) → m
  9. OrthogonalLine(J, m) → i
  10. OrthogonalLine(K, i) → l
  11. Mirror(l, m) → l'
  12. Line(M, N) → q
  13. OrthogonalLine(B, u, xOyPlane) → g
  14. OrthogonalLine(F, l) → n
  15. Intersect(l, n) → Q
  16. Line(P_1, g) → g_2
  17. Line(E, I) → j
  18. OrthogonalLine(L, i) → t
  19. Intersect(t, i) → O
  20. Line(D, b) → f
  21. Intersect(g_2, i) → S
  22. Line(S, j) → k
  23. OrthogonalLine(R, s) → j_4
  24. Intersect(j_4, i) → P
  25. LineBisector(P, O) → n_1
  26. OrthogonalLine(M_1, b) → m_1
  27. Line(H, q) → a
  28. Line(V, i) → d
  29. Line(W, d) → e
  30. Intersect(q, e) → Z
  31. Intersect(j, j_4) → T
  32. LineBisector(T, Z) → i_1
  33. Intersect(i_1, r) → F_1
  34. CircleArc(F_1, T, Z) → e_1
  35. OrthogonalLine(G, l) → p
  36. Mirror(J, m) → J'
  37. Intersect(g, r) → C
  38. Polygon(A_1, C, B, A) → q1, a_1, c, b_1, a_2
  39. OrthogonalLine(V_1, s) → h
  40. Line(B_1, e) → f_1
  41. Intersect(e_1, a) → C_1,
  42. LineBisector(C_1, Z) → g_1
  43. Intersect(k, e_1) → U,
  44. LineBisector(T, U, xOyPlane) → h_1
  45. Intersect(k, r) → D_1
  46. Intersect(r, g_1) → E_1
  47. CircleArc(E_1, C_1, Z) → d_1
  48. Intersect(l, j) → G_1
  49. Intersect(q, m_2) → H_1
  50. LineBisector(G_1, H_1) → j_1
  51. Intersect(r, j_1) → I_1
  52. CircleArc(I_1, G_1, H_1) → k_1
  53. Intersect(a, d) → K_1
  54. Intersect(k, j_4) → J_1
  55. LineBisector(J_1, K_1, xOyPlane) → l_1
  56. Intersect(l_1, a_1) → L_1
  57. CircleArc(L_1, J_1, K_1, xOyPlane) → p_1
  58. Intersect(k, a) → N_1
  59. Polygon(T, E, D_1, U) → q2, q_1, t_1, h_2, i_2
  60. Intersect(a, r) → O_1
  61. Polygon(M, D_1, N_1, C_1, Z) → poly1, r_1, s_1, f_2, j_2, k_2
  62. CircleArc(E_1, T, U, xOyPlane) → c_1
  63. Intersect(b, k) → R_1
  64. Polygon(R_1, J_1, G_1, I) → q3, l_2, n_2, p_2, i_3
  65. Polygon(H, N, H_1, K_1) → q4, h_3, n_3, q_2, r_2
  66. Polygon(J_1, K_1, H_1, G_1) → q5, s_2, t_2, b_2, c_2
  67. Polygon(U, N_1, C_1) → t1, d_2, u_1, e_2
  68. Intersect(l, s) → S_1
  69. CircleSector(Q, F, S_1) → c_3
  70. Mirror(c_3, m) → d_3
  71. Mirror(d_3, i) → e_3
  72. Mirror(c_3, i) → f_3
  73. Polygon(F, Q, S_1, A) → q6, f_4, q_3, g_3, a_3
  74. Mirror(F, i) → F'
  75. Mirror(Q, i) → Q'
  76. Mirror(S_1, i) → T_1
  77. Mirror(A, i) → A'
  78. Polygon(F', Q', T_1, A') → q6', f', q', j_3, a'
  79. Mirror(F, m) → F'_1
  80. Mirror(Q, m) → Q'_1
  81. Mirror(S_1, m) → U_1
  82. Mirror(A, m) → A'_1
  83. Polygon(F'_1, Q'_1, U_1, A'_1) → q6'_1, f'_1, q'_1, k_3, a'_1
  84. Mirror(F'_1, i) → W_1
  85. Mirror(Q'_1, i) → Z_1
  86. Mirror(U_1, i) → A_2
  87. Mirror(A'_1, i) → B_2
  88. Polygon(W_1, Z_1, A_2, B_2) → q7, w_1, z_1, l_3, m_3
  89. Mirror(F', a') → F''
  90. Mirror(A', a') → A''

AI Drawing Prompt Reference

Draw a complex 2D shape involving multiple circles, vectors, and angles. Start by drawing a line segment and its perpendicular line. Then, create a vector from the line segment and find its orthogonal vector. Use these elements to construct various geometric objects like midpoints, angle bisectors, mirror reflections, and circular arcs. Finally, combine these objects into a polygon to showcase the intricate geometric construction and spatial relationships.
The prompt above was compiled from the original drawing commands and is for reference only.